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From Streaks to Spots and on to Turbulence: Exploring the Dynamics of Boundary Layer Transition

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Abstract

“...an eerie type of chaos can lurk just behind a facade of order, and yet deep inside the chaos lurks an even eerier type of order.” Douglas Hofstadter

Bypass transition to turbulence in boundary layers is examined using linear theory and direct numerical simulations (DNS). First, the penetration of low-frequency free-stream disturbances into the boundary layer is explained using a model problem with two time scales, namely the shear and wall-normal diffusion. The simple model provides a physical understanding of the phenomenon of shear sheltering. The second stage in bypass transition is the amplification of streaks. Streak detection and tracking algorithms were applied to examine the characteristics of the streak population inside the boundary layer, beneath free-stream turbulence. It is demonstrated that simple statistical averaging masks the wealth of streak amplitudes in transitional flows, and in particular the high-amplitude, relatively rare events that precede the onset of turbulence. The third stage of the transition process, namely the secondary instability of streaks, is examined using secondary instability analysis. It is demonstrated that two types of instability are possible: An outer instability arises near the edge of the boundary layer on the lifted, low-speed streaks. An inner instability also exists, and has the appearance of a near-wall wavepacket. The stability theory is robust, and can predict the particular streaks which are likely to undergo secondary instability and break down in transitional boundary layers beneath free-stream turbulence. Beyond the secondary instability, turbulent spots are tracked in DNS in order to examine their characteristics in the subsequent non-linear stages of transition. At every stage, we compare the findings from linear theory to the empirical observations from direct solutions of the Navier-Stokes equations. The complementarity between the theoretical predictions and the computational experiments is highlighted, and it leads to a detailed view of the mechanics of transition.

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  1. Department of Mechanical Engineering, Imperial College London, London, SW7 2AZ, UK

    Tamer A. Zaki

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Zaki, T.A. From Streaks to Spots and on to Turbulence: Exploring the Dynamics of Boundary Layer Transition. Flow Turbulence Combust 91, 451–473 (2013). https://doi.org/10.1007/s10494-013-9502-8

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  • DOI: https://doi.org/10.1007/s10494-013-9502-8

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